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Math Help - Two very irritating area problems. (polar, and restricted area)

  1. #1
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    Two very irritating area problems. (polar, and restricted area)

    hi guys

    1. A curve is given in polar coordinates of r = cos ^ 2 fi , 0 <= fi <= 2 pi
    How big area does the place/area have which is enclosed by the curve?.


    2. calculate the area of the restricted area which is located between the curves y = x^3 and y = x^4.

    Ok as far as I am concerned you don't necesserily need to draw this in x and y axis do I? the thing is how to get to know the limits of integration analytically ? I am very bad at finding stuff like this in graphical solutions
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  2. #2
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    Quote Originally Posted by reaz View Post
    hi guys

    1. A curve is given in polar coordinates of r = cos ^ {2}({\phi}) , \;\ 0 <= {\phi} <= 2 {\pi}
    How big area does the place/area have which is enclosed by the curve?.
    That is 'phi'(the Greek letter). Not 'fi', as in "fee-fi-fo-fum, I smell the blood of an....".

    Wait, before I finish that, you aren't an Englishman, are you?.

    Anyway, Just use the polar integration thingy.

    \frac{1}{2}\int_{0}^{2\pi}cos^{4}({\phi})d{\phi}
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  3. #3
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by reaz View Post
    hi guys

    1. A curve is given in polar coordinates of r = cos ^ 2 fi , 0 <= fi <= 2 pi
    How big area does the place/area have which is enclosed by the curve?.


    2. calculate the area of the restricted area which is located between the curves y = x^3 and y = x^4.

    Ok as far as I am concerned you don't necesserily need to draw this in x and y axis do I? the thing is how to get to know the limits of integration analytically ? I am very bad at finding stuff like this in graphical solutions
    For the second question,

     \int_0^1 dx \int_{x^4}^{x^3} dy

    Where the dx domain comes from equating  x^3 = x^4

    These are equal at 0 and 1. But notice on the interval  0 \le x \le 1 that  x^4 \le x^3

    So our dy domain is from  x^4 to  x^3
    Last edited by AllanCuz; May 25th 2010 at 04:49 AM.
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    ... Englishman, Be he alive, or be he dead. I'll have his bones to grind my bread ^^


    Anyway thanks for the hints I will try to proceed from what's been given by u guys.
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